you should be able to replace the inner body of the tap with a standard body, as it should be a half inch or 15mm inner body, looks like the shaft is broken in half, so when you turn it on the bottom half of the shaft sticks down,till the pressure of the water pushes it up after a min or two, you have to turn the water off, and drain off that tap, them take the cap off, unscrew the cover of the tap, so you can see the inner part of the tap, get a 15mm spanner and unscrew the tap in half, take the inner body that has the shaft and washer on it,to your hardwear and get the the same one that has the same tread on it 15mm, and screw it back into the tap and your done, what your doing is takeing the tap in half..but make sure to hold the tap as your unscrewing it in half, you dont want to crack the sink,, not a hard job to do,,
j, October 2014